Since this is basically the same question as the one on Sci-Fi I will summarize the answer from @Valorum.
Basically, some wear underwear, some don't even go that far. Valorum gives more quotes (I encourage you to take a look at his answer), but I feel that these are the best examples.
From The Order of the Phoenix, here's an example with underwear:
Snape was hanging upside-down in the air, his robes falling over his head to reveal skinny, pallid legs and a pair of greying underpants.
From The Goblet of Fire, an example without underwear:
Harry, Ron and Hermione joined it, right behind a pair of men who were
having a heated argument. One of them was a very old wizard who was
wearing a long flowery nightgown. The other was clearly a Ministry
wizard; he was holding out a pair of pinstriped trousers and almost
crying with exasperation. ‘Just put them on, Archie, there’s a good
chap, you can’t walk around like that, the Muggle on the gate’s
already getting suspicious –’ ‘I bought this in a Muggle shop,’ said
the old wizard stubbornly. ‘Muggles wear them.’ ‘Muggle women wear
them, Archie, not the men, they wear these,’ said the Ministry wizard,
and he brandished the pinstriped trousers. ‘I’m not putting them on,’
said old Archie in indignation. ‘I like a healthy breeze round my
All credit to Valorum for this, he did the work.